In the field of petroleum well drilling and logging, resistivity logging tools are frequently used to provide an indication of the electrical resistivity of rock formations surrounding an earth borehole. Such information regarding resistivity is useful in ascertaining the presence or absence of hydrocarbons. A typical resistivity logging tool includes a transmitter antenna and a pair of receiver antennas located at different distances from the transmitter antenna along the axis of the tool. The transmitter antenna is used to create electromagnetic fields in the surrounding formation. In turn, the electromagnetic fields in the formation induce an electrical voltage in each receiver antenna. Due to geometric spreading and absorption by the surrounding earth formation, the induced voltages in the two receiving antennas have different phases and amplitudes. Experiments have shown that the phase difference (Φ) and amplitude ratio (attenuation, A) of the induced voltages in the receiver antennas are indicative of the resistivity of the formation.
Many formations have resistive anisotropy, a property which is generally attributable to extremely fine layering during the sedimentary build-up of the formation. Hence, in a coordinate system oriented such that the x-y plane is parallel to the formation layers and the z axis is perpendicular to the formation layers, resistivities Rx and Ry in directions x and y, respectively, are the same, but resistivity Rz in the z direction is different from Rx and Ry. The resistivity in a direction parallel to the plane of the formation (i.e., the x-y plane) is known as the horizontal resistivity, Rh, and the resistivity in the direction normal (i.e., perpendicular) to the plane of the formation (the z direction) is known as the vertical resistivity, Rv. The index of anisotropy, λ, is defined as λ=[Rv/Rh]1/2.
The relative dip angle, α, is the angle between the tool axis and the normal to the plane of the formation. Resistive anisotropy and relative dip angle each have significant but complex effects on resistivity logging tool measurements. Various techniques have been developed for extracting resistivity and dip information from tool measurements, including U.S. Pat. No. 6,393,364, titled “Determination of conductivity in anisotropic dipping formations from magnetic coupling measurements” by inventors L. Gao and S. Gianzero. As an iterative technique based on an analytical analysis of the logging environment, Gao and Gianzero's technique offers a fast conversion of measurement information to formation parameter information that is reliable and that works over a extended range of possible formation parameter values. However, their technique relies heavily on a “diagonal” coupling measurement, i.e., a measurement between parallel transmitter and receiver antennas. In many logging tools, this measurement is undesirably sensitive to small dimensional changes in the tool, e.g., those caused by thermal expansion or contraction and those caused by mechanical impacts or vibration, making it unduly difficult to obtain accurate formation information from the logging tool measurements.
By way of example, specific system and method embodiments are shown in the drawings and are described in detail below. It should be understood, however, that the drawings and detailed description are not intended to limit the disclosure, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the scope of the appended claims.